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1. Introduction

Reliability refers to the ability of a system or component to perform consistently without failure over its expected lifetime. In server environments, reliability is crucial as downtime can lead to significant business disruptions and financial loss. Reliability analysis helps measure dependability by estimating expected failures, calculating Mean Time Between Failures (MTBF), and evaluating overall system performance. For servers like the Dell PowerEdge R650, such analysis provides valuable insights into failure trends, operational risks, and long-term performance, ensuring organizations can plan effectively for continuous, mission-critical operations.

2. Data Summary

The reliability analysis of the Dell PowerEdge R650 server is based on the following data and assumptions:

Parameter	Value
Total Servers Sold Annually (All Models)	2,000,000 units
Percentage of R-series Servers	40%
Percentage of R650 Servers within R-series	15%
R650 Server Failure Rate	1%

3. Assumptions

Servers are assumed to operate continuously (24×7) throughout the year.
The failure rate is considered constant during the analysis period.
All servers are deployed under standard enterprise operating conditions.

4. Annual Failure Rate Calculation

The failure rate analysis provides an estimate of the number of Dell PowerEdge R650 servers expected to fail annually based on the provided sales data and reported failure rate. This step is essential in reliability engineering, as it allows organizations to anticipate hardware issues, plan for spare units, and design appropriate maintenance strategies. The below calculation provides the total number of R650 servers expected to fail each year based on the provided data.

4.1 Total R-series Servers Sold

The number of R-series servers sold by taking 40% of the total servers sold is

$$ \begin{align*} \text{Number of R-Series Servers Sold} &= 20,00,000 \times 0.40 \\ &= 8,00,000 \text{ servers} \end{align*} $$

4.2 Total R650 Servers Sold

This step identifies the number of R650 models sold by taking 15% of the total R-series sales.

$$ \begin{align*} \text{Number of R650 Servers Sold} &= 8,00,000 \times 0.15 \\ &= 1,20,000 \text{ servers} \end{align*} $$

4.3 Number of R650 Server Failures

The 1% failure rate to the total number of R650 servers sold.

$$ \begin{align*} \text{Number of R650 Servers Failures} &= 1,20,000 \times 0.01 \\ &= 1,200 \text{ failures} \end{align*} $$

5. Mean Time Between Failures (MTBF)

The Mean Time Between Failures (MTBF) is a key reliability metric used to evaluate the expected operational lifespan of a system before a failure occurs. It represents the average time interval between successive failures across a large population of deployed units under normal operating conditions. While MTBF does not guarantee an individual unit’s lifetime, it provides a statistical benchmark for assessing hardware reliability.

Formula:
The formula to calculate Mean Time Between Failures (MTBF) is given as,

$$ \begin{align*} \text{MTBF} &= \frac {\text{Total Operational Time}} {\text{Number of failures}} \end{align*} $$

5.1 Total Operational Time

This represents the cumulative hours of operation for all R650 servers sold in a year. Assuming each server operates continuously (24 hours a day, 365 days a year), then the total operational time is as follows:

$$ \begin{align*} \text{Total Operational Time} &= \text{R650 servers sold} \times 0.24 \times 365 \\ &= 1,20,000 \times 24 \times 365 \\ &= 1,05,12,00,000 \text{ hours} \\ \end{align*} $$

5.2 Number of Failures

From the Failure Rate Calculation, the expected number of annual server failures is given below.

$$ \begin{align*} \text{Number of Server Failures} &= 1,200 \text{ Servers} \\ \end{align*} $$

6. Mean Time Between Failure (MTBF) Calculation

6.1 MTBF in Hours

$$ \begin{align*} \text{MTBF} &= \frac{1,05,12,00,000}{1200 \text{ failures}} \\ &=8,76,000 \text{ hours} \\ \end{align*} $$

6.2 MTBF in Years

$$ \begin{align*} \text{MTBF} &= \frac{8,76,00,000}{24 \times 365} \\ &=100 \text{ years} \\ \end{align*} $$

7. Conclusion

The reliability analysis of the Dell PowerEdge R650 server indicates that out of an estimated 120,000 units sold annually, approximately 1,200 servers are expected to fail each year, based on a 1% failure rate. The calculated Mean Time Between Failures (MTBF) is 876,000 hours, or about 100 years, which reflects the strong engineering and dependability of the system.